On asymptotic stability of nonlinear waves
Séminaire Laurent Schwartz — EDP et applications (2016-2017), Talk no. 18, 27 p.

We review some results on asymptotic stability of nonlinear waves for a few dispersive or wave models, like the nonlinear Schrödinger equation, the generalized Korteweg-de Vries equation, and the nonlinear wave and Klein-Gordon equations. Then, we focus on recent results of the authors concerning the asymptotic stability of the kink for the ${\phi }^{4}$ equation under odd perturbations. We also present two results (one of which seems previously unknown) of non-existence of small breathers for some nonlinear Klein-Gordon equations.

Published online:
DOI: 10.5802/slsedp.111
Kowalczyk, Michał 1; Martel, Yvan 2; Muñoz, Claudio 1

1 Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático CNRS, Universidad de Chile Santiago Chile
2 CMLS, École Polytechnique, CNRS, Université Paris-Saclay Route de Saclay 91128 Palaiseau Cedex France
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Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio. On asymptotic stability of nonlinear waves. Séminaire Laurent Schwartz — EDP et applications (2016-2017), Talk no. 18, 27 p. doi : 10.5802/slsedp.111. http://archive.numdam.org/articles/10.5802/slsedp.111/

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